From the given transfer characteristic of a transistor in $\mathrm{CE}$ configuration, the value of power gain of this configuration is ${10}^x$, for $R_B=10 \mathrm{k\Omega }$, and $R_C=1 \mathrm{k\Omega }$. The value of $x$ is _____.

The formula to calculate the current gain $\left(\beta \right)$ in CE configuration is given by

$\beta =\frac{∆I_C}{∆I_B} ...\left(1\right)$

Considering the third and the first points on the given graph, the current gain can be calculated as follows:

$\begin{array}{rcl}\beta & =& \frac{\left(30-10\right)\times {10}^{-3} \mathrm{A}}{\left(300-100\right)\times {10}^{-6} \mathrm{A}}\\ & =& 100\end{array}$

The formula to calculate the power gain $\left(P\right)$ in CE mode can be written as

$P={\beta }^2·\frac{R_C}{R_B} ...\left(2\right)$

Substitute the known values of the parameters into equation (2) and solve to calculate the required unknown parameter.

$\begin{array}{rcl}{10}^x& =& {100}^2\times \frac{1 \mathrm{k\Omega }}{10 \mathrm{k\Omega }}\\ & =& 1000\\ & =& {10}^3\\ & \Rightarrow & x=3\end{array}$